What does extremum mean?
An extremum is the highest or lowest value that a function, quantity, or variable attains. The word is chiefly mathematical: in calculus, an extremum occurs where a function reaches a peak (a maximum) or a trough (a minimum), and analysts distinguish local extrema, which are extreme only relative to neighboring points, from global extrema, which are extreme across the entire domain. Beyond pure mathematics, the term appears in optimization, statistics, physics, and engineering wherever identifying limiting values matters — for example, finding the extremum of a cost function or a temperature curve. Formal and precise in register, it is rarely heard in casual speech, where simpler words such as "peak," "high," or "low" do the work. Its Latin plural is "extrema." For students of mathematics and science, however, "extremum" is indispensable vocabulary, condensing the twin ideas of greatest and least into one exact term.
nounThe greatest or least value attained by a function or quantity; a maximum or minimum point. In mathematics, it denotes a point at which a function reaches either its highest or lowest value, whether locally or globally.
- A mathematical maximum or minimum value of a function, either local (relative to nearby points) or global (absolute over the entire domain).
- More generally, the greatest or least value that any quantity or variable can attain.
"Calculus students learn to locate each extremum of a curve by finding where its derivative equals zero."
"The algorithm searches the parameter space for the global extremum of the cost function."
"Temperatures at the research station reached an extremum not seen in decades."
The standard plural follows the Latin second-neuter declension; the anglicized "extremums" is occasionally seen but widely considered nonstandard in technical writing.
"The function has two local extrema within the interval [0, 10]."
Every mountain peak and ocean trench on a graph has one thing in common: mathematicians call them all extrema — and calculus finds them without ever climbing a single slope.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of extremum
"Extremum" comes directly from Latin extremus, the superlative of exter (or exterus), meaning "outermost" or "farthest," which also gives English "extreme" and "extremity." The term entered scientific English in the early modern period as mathematicians sought a neutral noun covering both maxima and minima. It shares this Latin root with cognates such as "extreme," "extremely," and "extremity," all preserving the sense of reaching the outer limit.
Related word forms
How extremum is actually used
Primarily a formal, technical term used in mathematics, statistics, optimization, and the physical sciences; rare in everyday conversation. The plural "extrema" follows the Latin second-declension pattern. Writers often prefer the plainer terms "maximum" and "minimum" outside technical contexts.
Easily confused with extremum
"Extreme" is an adjective meaning very great in degree, while "extremum" is a noun naming the specific maximum or minimum value itself.